tomleslie

5565 Reputation

17 Badges

10 years, 1 days

MaplePrimes Activity


These are answers submitted by tomleslie

and use list declarations for the various options, like 'color' etc. As in the attached

PS The plot renders better in a MAple worksheet than it does on this webpage - honest!

  restart;
  with(plots):
  implicitplot
  ( eval( [ x^3+y^3-3*a*x*y=0,
            x+y+a=0
          ],
          a=1
        ),
    x=-3..3,
    y=-3..3,
    color=[red, blue],
    linestyle=[1, 6],
    thickness=[2, 2],
    numpoints=10000
  )

 

 

 

Download folium.mw

in Maple 2019. I can reproduce the same error in Maple18. It has something(?) to do with how 'Pi' is treated in some expressions - which I haven't fully diagnosed.

I can make the problem "go away" by including the statement

myPi:=evalf(Pi)

and replacing all occurrences of 'Pi' in the worksheet with 'myPi'. This now gives the same solution in Maple 18 as your original (unaltered) worksheet provides in Maple 2019. Check the attached

restart

mbal := 0.28e-2:

rbal := 0.2e-1:

Cw := .47:

g := 9.81:

myPi := evalf(Pi)

3.141592654

(1)

A := myPi*rbal^2:

beta := 3.33*myPi*(1/180):

s0x := .2:

s0y := .25:

rho := 1.293:

l := 2:

vx := diff(sx(t), t);

diff(sx(t), t)

(2)

vy := diff(sy(t), t);

diff(sy(t), t)

(3)

ax := diff(sx(t), `$`(t, 2));

diff(diff(sx(t), t), t)

(4)

ay := diff(sy(t), `$`(t, 2));

diff(diff(sy(t), t), t)

(5)

v0x := cos(beta)*v0;

.9983115393*v0

(6)

v0y := sin(beta)*v0;

0.5808674961e-1*v0

(7)

`ΣFx` := -Fdx = mbal*ax;

-Fdx = 0.28e-2*(diff(diff(sx(t), t), t))

(8)

`ΣFy` := -Fz-Fdy = mbal*ay;

-Fz-Fdy = 0.28e-2*(diff(diff(sy(t), t), t))

(9)

Fz := mbal*g;

0.27468e-1

(10)

Fdx := .5*rho*vx^2*A*Cw;

0.3818354544e-3*(diff(sx(t), t))^2

(11)

Fdy := .5*rho*vy^2*A*Cw;

0.3818354544e-3*(diff(sy(t), t))^2

(12)

ics1 := sx(0) = s0x, (D(sx))(0) = v0x;

sx(0) = .2, (D(sx))(0) = .9983115393*v0

(13)

ics2 := sy(0) = s0y, (D(sy))(0) = v0y;

sy(0) = .25, (D(sy))(0) = 0.5808674961e-1*v0

(14)

verplaatsingx := dsolve({ics1, `ΣFx`}, sx(t));

sx(t) = (1750000000/238647159)*ln((2382442126508618487/17500000000000000000)*v0*exp(238647159/8750000000)*t+exp(238647159/8750000000))

(15)

verplaatsingy := dsolve({ics2, `ΣFy`});

sy(t) = 1/4+(875000000/238647159)*ln((1/505799395325000000000000000000000000000)*(154024864110787311*sin((9/3500000)*202319758130^(1/2)*t)*v0+50000000000000*202319758130^(1/2)*cos((9/3500000)*202319758130^(1/2)*t))^2)

(16)

eindy := rhs(verplaatsingy) = rbal;

1/4+(875000000/238647159)*ln((1/505799395325000000000000000000000000000)*(154024864110787311*sin((9/3500000)*202319758130^(1/2)*t)*v0+50000000000000*202319758130^(1/2)*cos((9/3500000)*202319758130^(1/2)*t))^2) = 0.2e-1

(17)

eindx := rhs(verplaatsingx) = l;

(1750000000/238647159)*ln((2382442126508618487/17500000000000000000)*v0*exp(238647159/8750000000)*t+exp(238647159/8750000000)) = 2

(18)

t := solve(eindy, t);

.8645823917*arctan(0.4101936496e16*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2), 0.4755738338e-18*(0.3833525074e60*v0^4+0.1634650611e65*v0^2+0.1742575415e69)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(3/2)/v0+0.2826442056e-49*(-0.3219605325e65*v0^2-0.1059539541e68)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2)/v0), .8645823917*arctan(-0.4101936496e16*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2), -0.4755738338e-18*(0.3833525074e60*v0^4+0.1634650611e65*v0^2+0.1742575415e69)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(3/2)/v0-0.2826442056e-49*(-0.3219605325e65*v0^2-0.1059539541e68)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2)/v0), .8645823917*arctan(0.4695984595e14*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2), 0.7135610645e-24*(0.3833525074e60*v0^4+0.1634650611e65*v0^2+0.1742575415e69)*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(3/2)/v0+0.3235771292e-51*(-0.3219605325e65*v0^2-0.1059539541e68)*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2)/v0), .8645823917*arctan(-0.4695984595e14*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2), -0.7135610645e-24*(0.3833525074e60*v0^4+0.1634650611e65*v0^2+0.1742575415e69)*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(3/2)/v0-0.3235771292e-51*(-0.3219605325e65*v0^2-0.1059539541e68)*(-1.*(-0.1500724738e32*v0^2-0.1003231945e35+137340.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2)/v0)

(19)

t := evalf(t[1]);

.8645823917*arctan(0.4101936496e16*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2), 0.4755738338e-18*(0.3833525074e60*v0^4+0.1634650611e65*v0^2+0.1742575415e69)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(3/2)/v0+0.2826442056e-49*(-0.3219605325e65*v0^2-0.1059539541e68)*((0.1966873837e28*v0^2+0.1314851828e31+18.*(0.1192836232e53*v0^4+0.1546333077e56*v0^2)^(1/2))/(0.8004529672e54*v0^4+0.3413205617e59*v0^2+0.3638556250e63))^(1/2)/v0)

(20)

v0 := fsolve(eindx, v0);

7.694586915

(21)

``

``


 

Download piProb.mw

is an "element" of the Maplet() - not of the Window(). So the following will work,

  restart;
  with(Maplets):
  with(Maplets[Elements]):

  mpt:= Maplet
        ( Window
          ( 'title' ="Точка выше или ниже прямой" ,
            [ ToggleButton[TB1]("Ta", 'group' = 'tb1'),
              ToggleButton[TB2]("Tb", 'group' = 'tb1')
            ]
          ),
          ButtonGroup['tb1']()
        ):
  Display(mpt);

 

Download mplt.mw

but something like

plot( diff( rhs(sol), x), x=0..10)

ought to get you close - depending on other "unknowns" which might appear in "sol". If you have other variables/parameters, say a, b, t then

plot( eval( diff( rhs(sol), x), [a=whatever1, b=whatever2, t=whatever3]), x=0..10)

If neither of the above solves your problem, then use the big green up-arrow in the Mapleprimes toolbar to upload a worksheet

is shown in the attached

eq1:=(1/2)*y*exp(-y)+2*y^3 - x*ln(x) +x^2 = 10:
eq2:=(1/2)*y*exp(-y)+2*y^3 +x^2 = 10 + x*ln(x):
eq3:=y*exp(-y)+4*y^3 - 2*x*ln(x) +2*x^2 = 20:

g:= z-> simplify( (lhs(z)-rhs(z))):
isEquiv:= (x,y)-> type(simplify(g(x)/g(y)),numeric):

isEquiv(eq1, eq2);
isEquiv(eq1, eq3);
isEquiv(eq2, eq3);

true

 

true

 

true

(1)

 


 

Download checkEquiv.mw

like this

`mod`~(<8, 9 ,9 ,7 ,9 ,10 ,5>^~(-1),11);

 

you have two lists, not two vectors. However the techniques for elementwise multiplication is pretty much the same for both, as shown in the attached


 

#
# Elementwise multiplication with lists
#
  X:=[x1 ,x2,x3];
  G:=[g1,g2,g3];
  X*~G

[x1, x2, x3]

 

[g1, g2, g3]

 

[x1*g1, x2*g2, x3*g3]

(1)

#
# Elementwise multiplication with vectors
#
  X:=<x1 ,x2,x3>;
  G:=<g1,g2,g3>;
  X*~G

Vector(3, {(1) = x1, (2) = x2, (3) = x3})

 

Vector(3, {(1) = g1, (2) = g2, (3) = g3})

 

Vector[column](%id = 18446744074778350406)

(2)

 


 

Download LorV.mw

if you really want to know about the methods used by Maple to factor large integers, then a good place to start is the help page for the command ?ifactor. Amongst other things, this will tell you

  1. when the quadratic sieve method is used and which other methods can be invoked
  2. where to find an explanation of the quadratic sieve (in the References, sub-section)

You appear to believe that the "prettyprinted" version of Maple's 2D-input bears a simple relationship to underlying ASCII characters - not true.

If you select the input argument to the Explode() command and then, from the Maple toolbar, you use

Format->Convert To->1-D Math Input,

then you will observe that your "input" string is actually

"1&le; n&le;m"

which the Explode() command explodes "correctly"

 

 

Ths problem has existed for the past couple of days :-(

NLPSolve() (usually) requires that the objective function be differentiable, o that it can figure out which direction represents "downhill". The "Error Message" just says that around the iniitial point the objective function is "flat". This *might* be a maximum, a minimum, or indeed just a region where your objective function is "flat", ie doesn't change value when the independent variables are changed

If you are supplying an initial point, change it

If you are not supplying an initial point, then try supplying a few different ones

Alternatively use the big green up-arrow in the MaplePrimes toolbar to upload your worksheet

You have defined 'Sol' as a set - ie using curly braces {}.

Sets have no concept of order - you cannot guarantee which element  will occur where. Whatever you may think, the set {3,2,1} is absolutely identical to {1, 2, 3}.

The simplest way to fix your immediate problem is to change the definition of 'Sol' from a set to a list. Although it defeats me why you should want to loop through the elements of either the list or the set, why not just apply the 'assign()' command elementwise??

Both options are shown in the attached

restart

N := 3; L := 0; R := 1; T := 1; NN := 4; Mx := NN; My := NN; Mz := NN; `&Delta;x` := (R-L)/Mx; `&Delta;y` := (R-L)/My; `&Delta;z` := (R-L)/Mz; `&Delta;t` := T/N; n := 0

1/4

 

1/4

 

1/4

 

1/3

(1)

Sol := [u[1, 1, 1, 1] = 0.14578485742667928362e-1, u[1, 1, 2, 1] = 0.29548584487036957497e-1, u[1, 1, 3, 1] = 0.44323688168892291723e-1, u[1, 2, 1, 1] = 0.29548584487036957496e-1, u[1, 2, 2, 1] = 0.59949352480274039874e-1, u[1, 2, 3, 1] = 0.90261881648876334312e-1, u[1, 3, 1, 1] = 0.44323688168892291724e-1, u[1, 3, 2, 1] = 0.90261881648876334322e-1, u[1, 3, 3, 1] = .13752578451379877709, u[2, 1, 1, 1] = 0.26717348328676609020e-1, u[2, 1, 2, 1] = 0.54613563612919064759e-1, u[2, 1, 3, 1] = 0.83815829643036530661e-1, u[2, 2, 1, 1] = 0.54613563612919064757e-1, u[2, 2, 2, 1] = .11170063733186747631, u[2, 2, 3, 1] = .17183586485000930908, u[2, 3, 1, 1] = 0.83815829643036530657e-1, u[2, 3, 2, 1] = .17183586485000930908, u[2, 3, 3, 1] = .26633149533104995811, u[3, 1, 1, 1] = 0.39827755588924378576e-1, u[3, 1, 2, 1] = 0.81803408890300879260e-1, u[3, 1, 3, 1] = .12733149048832359596, u[3, 2, 1, 1] = 0.81803408890300879254e-1, u[3, 2, 2, 1] = .16807855529017971428, u[3, 2, 3, 1] = .26194706234064804568, u[3, 3, 1, 1] = .12733149048832359595, u[3, 3, 2, 1] = .26194706234064804570, u[3, 3, 3, 1] = .40978986410708023066]

[u[1, 1, 1, 1] = 0.14578485742667928362e-1, u[1, 1, 2, 1] = 0.29548584487036957497e-1, u[1, 1, 3, 1] = 0.44323688168892291723e-1, u[1, 2, 1, 1] = 0.29548584487036957496e-1, u[1, 2, 2, 1] = 0.59949352480274039874e-1, u[1, 2, 3, 1] = 0.90261881648876334312e-1, u[1, 3, 1, 1] = 0.44323688168892291724e-1, u[1, 3, 2, 1] = 0.90261881648876334322e-1, u[1, 3, 3, 1] = .13752578451379877709, u[2, 1, 1, 1] = 0.26717348328676609020e-1, u[2, 1, 2, 1] = 0.54613563612919064759e-1, u[2, 1, 3, 1] = 0.83815829643036530661e-1, u[2, 2, 1, 1] = 0.54613563612919064757e-1, u[2, 2, 2, 1] = .11170063733186747631, u[2, 2, 3, 1] = .17183586485000930908, u[2, 3, 1, 1] = 0.83815829643036530657e-1, u[2, 3, 2, 1] = .17183586485000930908, u[2, 3, 3, 1] = .26633149533104995811, u[3, 1, 1, 1] = 0.39827755588924378576e-1, u[3, 1, 2, 1] = 0.81803408890300879260e-1, u[3, 1, 3, 1] = .12733149048832359596, u[3, 2, 1, 1] = 0.81803408890300879254e-1, u[3, 2, 2, 1] = .16807855529017971428, u[3, 2, 3, 1] = .26194706234064804568, u[3, 3, 1, 1] = .12733149048832359595, u[3, 3, 2, 1] = .26194706234064804570, u[3, 3, 3, 1] = .40978986410708023066]

(2)

for i while i <= Mx-1 do for j while j <= My-1 do for k while k <= Mz-1 do u[i, j, k, n+1] := rhs(op((Mz-1)*((My-1)*(i-1)+j-1)+k, Sol)) end do end do end do

u[3, 2, 3, 1]

.26194706234064804568

(3)

restart;

N := 3: L := 0: R := 1: T := 1:
NN := 4: Mx := NN: My := NN: Mz := NN:
Delta__x := (R - L)/Mx; Delta__y := (R - L)/My;
Delta__z := (R - L)/Mz; Delta__t := T/N;
n := 0:
Sol := [u[1, 1, 1, 1] = 0.014578485742667928362, u[1, 1, 2, 1] = 0.029548584487036957497, u[1, 1, 3, 1] = 0.044323688168892291723,
        u[1, 2, 1, 1] = 0.029548584487036957496, u[1, 2, 2, 1] = 0.059949352480274039874, u[1, 2, 3, 1] = 0.090261881648876334312,
        u[1, 3, 1, 1] = 0.044323688168892291724, u[1, 3, 2, 1] = 0.090261881648876334322, u[1, 3, 3, 1] = 0.13752578451379877709,
        u[2, 1, 1, 1] = 0.026717348328676609020, u[2, 1, 2, 1] = 0.054613563612919064759, u[2, 1, 3, 1] = 0.083815829643036530661,
        u[2, 2, 1, 1] = 0.054613563612919064757, u[2, 2, 2, 1] = 0.11170063733186747631,  u[2, 2, 3, 1] = 0.17183586485000930908,
        u[2, 3, 1, 1] = 0.083815829643036530657, u[2, 3, 2, 1] = 0.17183586485000930908,  u[2, 3, 3, 1] = 0.26633149533104995811,
        u[3, 1, 1, 1] = 0.039827755588924378576, u[3, 1, 2, 1] = 0.081803408890300879260, u[3, 1, 3, 1] = 0.12733149048832359596,
        u[3, 2, 1, 1] = 0.081803408890300879254, u[3, 2, 2, 1] = 0.16807855529017971428,  u[3, 2, 3, 1] = 0.26194706234064804568,
        u[3, 3, 1, 1] = 0.12733149048832359595,  u[3, 3, 2, 1] = 0.26194706234064804570,  u[3, 3, 3, 1] = 0.40978986410708023066];

1/4

 

1/4

 

1/4

 

1/3

 

[u[1, 1, 1, 1] = 0.14578485742667928362e-1, u[1, 1, 2, 1] = 0.29548584487036957497e-1, u[1, 1, 3, 1] = 0.44323688168892291723e-1, u[1, 2, 1, 1] = 0.29548584487036957496e-1, u[1, 2, 2, 1] = 0.59949352480274039874e-1, u[1, 2, 3, 1] = 0.90261881648876334312e-1, u[1, 3, 1, 1] = 0.44323688168892291724e-1, u[1, 3, 2, 1] = 0.90261881648876334322e-1, u[1, 3, 3, 1] = .13752578451379877709, u[2, 1, 1, 1] = 0.26717348328676609020e-1, u[2, 1, 2, 1] = 0.54613563612919064759e-1, u[2, 1, 3, 1] = 0.83815829643036530661e-1, u[2, 2, 1, 1] = 0.54613563612919064757e-1, u[2, 2, 2, 1] = .11170063733186747631, u[2, 2, 3, 1] = .17183586485000930908, u[2, 3, 1, 1] = 0.83815829643036530657e-1, u[2, 3, 2, 1] = .17183586485000930908, u[2, 3, 3, 1] = .26633149533104995811, u[3, 1, 1, 1] = 0.39827755588924378576e-1, u[3, 1, 2, 1] = 0.81803408890300879260e-1, u[3, 1, 3, 1] = .12733149048832359596, u[3, 2, 1, 1] = 0.81803408890300879254e-1, u[3, 2, 2, 1] = .16807855529017971428, u[3, 2, 3, 1] = .26194706234064804568, u[3, 3, 1, 1] = .12733149048832359595, u[3, 3, 2, 1] = .26194706234064804570, u[3, 3, 3, 1] = .40978986410708023066]

(4)

  assign~(Sol):
#
# A test
#
  u[3, 2, 3, 1];

.26194706234064804568

(5)

 

 

 

Download listNotSet.mw

Force the timestep option to be 1/2 of the spacestep option, and it always seems to "work", irrespective of the magnitude of the latter.

The attached works for all values of "myStep" which I have tried.

I could speculate on why - so (at the risk of being completely wrong). SInce the spatial domain is symmetrical wrt 0, a spacestep setting of 0.1, would give 20 intervals. To guarantee 20 intervals in time, the timestep has to be set to 0.05. Maybe when computing a "default" timestep, Maple just uses the spacestep setting (ie 0.1), ignoring the spatial range, and thus ends up with 10 time intervals?

In general things seem to work better if the number of time intervals = number of spatial intervals

PS I also "corrected" the definition of the piecewise function used for the initial conditions, because I didin't understand wht yo menat by the condition 'true', and it was undefined for x=0

Anyhow for what it is worth the attached seems to work OK.


 

restart;
pde := diff(u(x,t),t$2)=diff(u(x,t),x$2):
bc  := u(-1,t)=u(1,t),D[1](u)(-1,t)=D[1](u)(1,t):
f:=x->piecewise( -1/2<x and x<0,
                 x+1/2,
                 x=0,
                 1/2,
                 0<x and x<1/2,
                 1/2-x,
                 0
               ):
plot(f(x),x=-1..1):
ic  := u(x,0)=f(x),D[2](u)(x,0)=0:
myStep:=1/100:
sol:=pdsolve( pde,
              { bc, ic },
              u(x,t),
              numeric,
              timestep=myStep/2,
              spacestep=myStep
            ):
sol:-animate(frames=50,t=0..1,title="time = %f");

 

 


 

Download pdeProb.mw

 

that the code you present is basically unfixable. Now just becuase I like making guesses, I'm going to make the following observations/recommendations

  1. learn the difference between a function with an argument nad an indexed variable: for example x(0) is the function x() with the argument 0, x[0] is the zeroth element of indexable variable 'x'. These are two entirely different concepts.  If you don't understand the difference, then don't write any code until you do!
  2. learn the difference between an indexable quantity (eg x[0]) and one with an inert subscript (eq x__0). If you choose to use Maple's 2D input option then this will "appear" the same in both input and output lines - although, of course, they have entirely different meanings. If you don't understand the difference, then don't write any code until you do!
  3. don't use the same name as the index variable in a "for" loop and then as the index variable in any statement (eg add() ) within that "for" loop. You *might* get away with this ( Maple's scoping rules are pretty good), but it is a high-risk activity.
  4. don't try to define a variable in terms of itself - for example in your code you have various places where you write something like x[n+1]=add(x[n], n=0..m). Note that this violates recommendation (3) above, but let's just assssume for the moment that Maple's scoping rules will handle this, and that the two quantities labelled 'n' on either side of this assignment are entirely distinct - so that (for example) Maple will (may?) interpret this as x[2]=add(x[n], n=0..m). Consider what happens if n=2 on the lhs and m=2. Then the statement becomes x[2]:=x[0]+x[1]+x[2]. So you are trying to assign x[2] in terms of itself. This is known as "recursive assignment" and will never work.
  5. If I guess what you actually mean when you commit any/all the errors above and try to fix it then I will get something like the attached. (I have also assumed that when you defined the parmeter 'u' and then never used it, you actually meant the parameter 'mu' which is used but never defined - of course this could be one of the many guesses where I'm wrong

Anyhow for what it is worth, the attached *might* be of some use - but you will have to check every single guess I have made

restart;
m := 10;
S[lambda] := sum(S[b]*lambda^b, b=0..m):
L[lambda]:= sum(L[b]*lambda^b, b=0..m):
G[lambda]:= S[lambda]*L[lambda]:
ft := unapply(G[lambda], lambda):
for i from 0 to m do
    A1[i] := (D@@i)(ft)(0)/i!;
end do;

10

 

S[0]*L[0]

 

L[0]*S[1]+L[1]*S[0]

 

L[0]*S[2]+L[1]*S[1]+L[2]*S[0]

 

L[0]*S[3]+L[1]*S[2]+L[2]*S[1]+L[3]*S[0]

 

L[0]*S[4]+L[1]*S[3]+L[2]*S[2]+L[3]*S[1]+L[4]*S[0]

 

L[0]*S[5]+L[1]*S[4]+L[2]*S[3]+L[3]*S[2]+L[4]*S[1]+L[5]*S[0]

 

L[0]*S[6]+L[1]*S[5]+L[2]*S[4]+L[3]*S[3]+L[4]*S[2]+L[5]*S[1]+L[6]*S[0]

 

L[0]*S[7]+L[1]*S[6]+L[2]*S[5]+L[3]*S[4]+L[4]*S[3]+L[5]*S[2]+L[6]*S[1]+L[7]*S[0]

 

L[0]*S[8]+L[1]*S[7]+L[2]*S[6]+L[3]*S[5]+L[4]*S[4]+L[5]*S[3]+L[6]*S[2]+L[7]*S[1]+L[8]*S[0]

 

L[0]*S[9]+L[1]*S[8]+L[2]*S[7]+L[3]*S[6]+L[4]*S[5]+L[5]*S[4]+L[6]*S[3]+L[7]*S[2]+L[8]*S[1]+L[9]*S[0]

 

L[0]*S[10]+L[1]*S[9]+L[2]*S[8]+L[3]*S[7]+L[4]*S[6]+L[5]*S[5]+L[6]*S[4]+L[7]*S[3]+L[8]*S[2]+L[9]*S[1]+L[10]*S[0]

(1)

beta:= 0.04: lambda:= 0.4: delta:= 0.3:
d:= 0.01: e:= 0.1: a:= 0.2: k:= 0.6:
mu:= 0.03: q:= 0.8:
x[0]:= 9: w[0]:= 3: y[0]:= 1: v[0]:= 4:
m := 3:

for n from 0 to m do
    x[n+1]:= x[0]+lambda*t-d*int(add(x[jj], jj=0..n), t=0..t)
             -
             beta*int(add(x[jj], jj=0..n)*x[n]*v[n], t=0..t);
    w[n+1]:= w[0]+(1-q)*beta*int(add(x[jj]*v[jj], jj=0..n), t=0..t)
             -
             e*int(add(w[jj], jj=0..n), t=0..t)
             -
             delta*int(add(w[jj], jj=0..n), t=0..t);
    y[n+1]:= y[0] + q*beta*int(add(x[jj]*v[jj], jj=0..n), t=0..t)
             -
             a*int(add(y[jj], jj=0..n), t=0..t)
             +
             delta*int(add(w[jj], jj=0..n), t=0..t);
    v[n+1]:= v[0] + k*int(add(y[jj], jj=0..n), t=0..t)
             -
             mu*int(add(v[jj], jj=0..n), t=0..t);
end do

9-12.65*t

 

3-.912*t

 

1+1.852*t

 

4+.48*t

 

9-25.70*t+25.83205000*t^2-.7681080000*t^4-6.348613332*t^3

 

3-1.824*t-0.1619200000e-1*t^3-0.272000000e-2*t^2

 

1+3.704*t-0.6476800000e-1*t^3-1.062480000*t^2

 

4+.96*t+.5484000000*t^2

 

9-38.75*t+78.65015000*t^2-90.72568551*t^3-27.42089744*t^5+62.64846853*t^4-0.1176547131e-2*t^11-0.2365939406e-1*t^10-0.5361510560e-1*t^9+.5664253416*t^8-1.763510425*t^7+7.623064696*t^6

 

3-2.736*t-0.4814062025e-3*t^7-0.5625284308e-2*t^6+0.7998712674e-2*t^5-0.2775993066e-1*t^4+.2070821333*t^3-0.145600000e-1*t^2

 

1+5.556*t-0.1925624810e-2*t^7-0.2250113723e-1*t^6+0.3199485070e-1*t^5-.1154925226*t^4+.8974378666*t^3-3.213040000*t^2

 

4+1.44*t+1.645200000*t^2-0.9715200000e-2*t^4-.2179800000*t^3

 

9-51.80*t+0.1992354573e-10*t^27+0.1296329103e-8*t^26+0.2643535147e-7*t^25+0.1127183443e-6*t^24-0.1989329580e-5*t^23-0.1355710429e-4*t^22+0.5938710560e-4*t^21+0.9247798360e-4*t^20-0.1107326654e-2*t^19+0.9847756904e-2*t^18-0.6836658000e-1*t^17+.3297720939*t^16-1.291286981*t^15+4.458073772*t^14-13.55133255*t^13+35.62626141*t^12-80.62369489*t^11+158.4926548*t^10-273.6418403*t^9+416.1169516*t^8-554.3659409*t^7+638.9342751*t^6-625.6821295*t^5+508.0768001*t^4-327.8484020*t^3+158.1663000*t^2

 

3-3.648*t+0.5715195343e-8*t^16+0.2593703940e-6*t^15+0.2138571915e-5*t^14-0.2119050938e-4*t^13-0.1555465514e-3*t^12+0.7784654894e-3*t^11-0.2956329137e-2*t^10+0.1567669086e-1*t^9-0.5394031369e-1*t^8+.1290831356*t^7-.2534910499*t^6+.4225449502*t^5-.6791878360*t^4+.9386432000*t^3-0.355200000e-1*t^2

 

1+7.408*t+0.2286078137e-7*t^16+0.1037481576e-5*t^15+0.8554287661e-5*t^14-0.8476203750e-4*t^13-0.6221862058e-3*t^12+0.3113861958e-2*t^11-0.1182531655e-1*t^10+0.6270676342e-1*t^9-.2158274481*t^8+.5154485692*t^7-1.012497769*t^6+1.684250728*t^5-2.667712024*t^4+4.028663467*t^3-6.451680000*t^2

 

4+1.92*t+3.290400000*t^2+.1265353300*t^4-.8770399998*t^3-0.1444218607e-3*t^8-0.1928668906e-2*t^7+0.3199485070e-2*t^6-0.1380081151e-1*t^5

(2)

``

Download adom.mw

of which the attached is only one

  restart;
  with(plots):
  with(plottools):
  d1:= display
       ( [ display
           ( circle
             ( [-6,0],
               6,
               color=red,
               thickness=2
             )
           ),
           plot( 6*sin(x),
                 x=0..4*Pi,
                 color=red,
                 thickness=2
               )
         ]
       ):
  F:= proc(t)
           display
           ( [ display
               ( line
                 ( [-6,0],
                   [6*cos(t)-6, 6*sin(t)],
                   color=blue,
                   thickness=4
                 )
               ),
               pointplot
               ( [t, 6*sin(t)],
                 symbol=solidcircle,
                 symbolsize=24,
                 color=blue
               )
             ],
             scaling=constrained
           );
      end proc:
   animate( F, [theta], theta=0..4*Pi, background=d1, frames=100);
        

 

 

Download anim.mw

 

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